Solving the quadratic equation, it is found that the duck was underwater for two seconds.
The path of the duck after x seconds is modeled by:
[tex]y = 2x^2 - 4x[/tex]
It is a concave up parabola, thus, the negative values of y, when he is underwater, are between the roots.
To find the roots:
[tex]y = 0[/tex]
[tex]2x^2 - 4x = 0[/tex]
[tex]2x(x - 2) = 0[/tex]
[tex]2x = 0 \rightarrow x = 0[/tex]
[tex]x - 2 = 0 \rightarrow x = 2[/tex]
2 - 0 = 2, thus, the duck was underwater for two seconds.
A similar problem is given at https://brainly.com/question/25181401
